BIMSA > BIMSA General Relativity Seminar Localized Deformations and Gluing Constructions in General Relativity
Localized Deformations and Gluing Constructions in General Relativity
Organizers
Lars Andersson , Bo Wen Zhao
Speaker
Hongyi Sheng
Time
Friday, September 20, 2024 10:30 AM - 11:30 AM
Venue
Online
Online
Zoom 559 700 6085 (BIMSA)
Abstract
Gluing constructions of initial data sets play an important role in general relativity. Earlier in 1979, Schoen-Yau used gluing constructions with conformal deformations as a crucial step in their proof of the famous positive mass theorem. Later Corvino modified the gluing constructions with a localized deformations, so that the structure of the manifold near infinity is well-preserved. In this talk, we will review some recent localized deformation theorems and their applications regarding rigidity and non-rigidity type results. We will then see that some results may be generalized to half space with boundary, thanks to our localized deformation techniques near the boundary. On the other hand, for the domains where localized deformation techniques are not valid (called non-generic domains), we will see that they are closely related to certain rigidity theorems.